Hydrate saturation estimation in the field is mainly controlled by proper interpretations of downhole electrical logging data based on Archie's law. However, saturation exponent value in Archie's law is site dependent, and its proper selection for hydrate-bearing sediments is still a challenge. In this study, a fractal model of saturation exponent is derived to show physical connections between saturation exponent and pore structure parameters. Hydrate saturation dependent pore-area and tortuosity fractal dimensions of effective pores to electrical conductivity are extracted from X-ray computed tomography (CT) images of xenon-hydrate-bearing alumina ball packings, and these values of pore structure parameters are applied to validate the model. Effects of hydrate saturation, intrinsic/primary pore structure parameters, and salt-removing effect due to hydrate formation on values of saturation exponent in Archie's law are discussed. Results and discussions show that model predicted and experimental values of formation factor in hydrate-free porous media are consistent; Pore-area fractal dimension of effective pores to electrical conductivity decreases while tortuosity fractal dimension increases with increasing hydrate saturation; The discrepancy in saturation exponent values is largely due to the different enhancement degrees of tortuosity due to hydrate formation; A larger intrinsic volume porosity, lower pore-area and tortuosity fractal dimensions, and the salt-removing effect due to hydrate formation all lead to a lower saturation exponent in Archie's law. This study has a great potential to facilitate interpretations of downhole electrical logging data in gas hydrate sites.

现场的水合物饱和度估算主要由根据阿奇定律对井下电测井数据的正确解释来控制。但是，阿奇定律中的饱和指数值是随位置而变的，对于含水合物沉积物的正确选择仍然是一个挑战。在这项研究中，导出了饱和指数的分形模型，以显示饱和指数与孔隙结构参数之间的物理联系。从含水合氙气的氧化铝球填料的X射线计算机断层扫描（CT）图像中提取有效孔的水合物饱和度相关的孔面积和曲折形分形维数，并利用这些孔结构参数值来验证模型。水合物饱和度，内在/主要孔隙结构参数的影响，讨论了水合物形成引起的除盐作用对阿奇定律中饱和指数的影响。结果与讨论表明，在无水合物的多孔介质中，模型预测值和形成因子的实验值是一致的。有效孔隙的孔隙率分形维数随水合物饱和度的增加而减小，而曲率分形维数随水合物饱和度的增加而增加。饱和指数值的差异主要是由于水合物形成导致曲折度的提高程度不同所致。较大的固有体积孔隙率，较低的孔隙率和曲折形分形维数以及由于水合物形成而引起的除盐效果均会导致阿奇定律的饱和指数较低。